Kagan told a University of Kentucky audience that she eventually took up the pastime after meeting with a Western senator. The lawmaker talked about the importance of hunting to his constituents and asked if she had ever hunted or fired a gun. She replied that she never had.

Kagan said she was “feeling a little punchy at the time” and told the senator she’d like to accompany him on a hunting trip.

The response from the senator was a “look of total horror” at the prospect of taking her along on one, she said.

Kagan, appointed in 2010 by President Barack Obama, promised to ask Scalia — an avid hunter — to take her hunting if she won confirmation. After joining the court, she recounted the story to Scalia. Thus began the hunting outings by the ideological opposites.

“I said this is the single promise I made” during her confirmation process, she said. “He thought it was hilarious.”

They started out by shooting clay pigeons together and then actual quail, pheasant. Last year, they moved up to hunting bigger game together — antelope in Wyoming, she said.

“I’ve enjoyed it,” she said. “I enjoy spending time with him. He’s a great guy.”

Scalia is not the only justice she socializes with. She said she and Justice Ruth Bader Ginsburg attend the opera together.

Asked about the cohesion of the current court, she said there have been times in the Supreme Court’s history when there was animosity among justices. That’s not the case now, she said.

“We really do like each other,” despite the sharp disagreements that sometimes divide justices, she said.

Kagan, the youngest and most recently appointed justice, fielded questions for an hour from UK’s law school dean and from students. Before joining the court, she served as solicitor general of the United States and dean of Harvard Law School, among other roles.

Asked about the significance of having three women as current members of the high court, she replied: “I honestly don’t think it makes much of a difference inside the conference room when we talk about a case, when we decide a case.”

But the presence of three female justices carries significance, she said, noting that none of the three “are shrinking violets.”

“It’s important for the institution, to show that women are a vital part of this profession, a vital part of this society,” Kagan said.

She also provided some behind-the-scenes insights into the court’s workings.

The justices have assigned seats when they meet in conference to review cases, she said.

Each justice is allowed a chance to talk about each case, and no one can speak twice until every member has spoken once, she said.

“Which is a very good rule if you’re the ninth person to speak,” Kagan said, referring to herself.

Once everyone has had a turn, she said, “free form” discussions often ensue.

But on some of the most important cases, that’s not always the case. In those situations, it’s often clear that justices have staked out their views and no one is “persuadable,” she said. In those cases, “each of us says our piece and then we leave it alone.”

“The only thing that further discussion is going to do is to get people annoyed at each other,” she said.

Kagan said that legal briefs written by lawyers generally carry more weight than oral arguments before the court. It’s rare that someone wins or loses a case during oral arguments, she said.

By the time a case is argued before the court, she said, “most people either have a strong view one way or at least are leaning.”